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705-805 (Hard)|   Geometry|      
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Bunuel
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a, b, and c are sides of a right triangle. What is the area of the tri 29 Jan 2016, 03:24
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C
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75% (hard)

Question Stats:

46% (01:33) correct 54% (01:19) wrong based on 81 sessions

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a, b, and c are sides of a right triangle. What is the area of the triangle?

(1) a = 4.
(2) a + b + c = 12
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C
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a, b, and c are sides of a right triangle. What is the area of the tri 29 Jan 2016, 05:47
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Bunuel
a, b, and c are sides of a right triangle. What is the area of the triangle?

(1) a = 4.
(2) a + b + c = 4.
Show more

Bunuel , is this question correct ?
(1) a = 4
We have no information on base or height
Not sufficient
(2) a + b + c = 4
Not sufficient
Combining 1 and 2 ,
b+c = 0
Area of \(\triangle\) = 0 as there is only side .


Answer C
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a, b, and c are sides of a right triangle. What is the area of the tri 29 Jan 2016, 05:52
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Bunuel
a, b, and c are sides of a right triangle. What is the area of the triangle?

(1) a = 4.
(2) a + b + c = 4.

Bunuel , is this question correct ?
(1) a = 4
We have no information on base or height
Not sufficient
(2) a + b + c = 4
Not sufficient
Combining 1 and 2 ,
b+c = 0
Area of \(\triangle\) = 0 as there is only side .


Answer C
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Edited. Thank you for noticing.
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a, b, and c are sides of a right triangle. What is the area of the tri 29 Jan 2016, 20:48
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Bunuel
a, b, and c are sides of a right triangle. What is the area of the triangle?

(1) a = 4.
(2) a + b + c = 12
Show more

Hi,

We know its a right angle triangle..


(1) a = 4.
this gives us just one side, clearly insuff

(2) a + b + c = 12
this gives the perimeter. again clearly insuff.

Combined..
we know one side is 4 and sum of two other sides is 12-4=8...
and these two sides are related by pythagorean theorem...
so it should be suff..

but lest find teh answer
the most important info we can gather from this is a is not the biggest/hypotenuse
so let b be the hypotenuse, so b= \(\sqrt{a^2+c^2}\)..
b= \(\sqrt{4^2+c^2}\)...
\(\sqrt{16+c^2}\)...
substitute in the sum of two other sides is 12-4=8...
c+\(\sqrt{16+c^2}\)=8..
\(\sqrt{16+c^2}\)=8-c..
16+c^2=(8-c)^2..
16+c^2=64+c^2-16c...
16c=48 or c=3...
area =3*4/2=6..
suff..
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a, b, and c are sides of a right triangle. What is the area of the tri 29 Jan 2016, 21:27
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[Alter to algebraic way
a+b+c = 12
c – hypotenuse

1.case
If C= 4 , hypotenuse cant be four ,since a or b will become higher than four to make a+b+c = 12
So 4 should a or b

2. case
Consider 4 as a or b
A + 4 + C = 12 from here we know 3,4,5 will fit
3+4+5 = 12 (area will be 6 units)
2+4+ 6 = 12 (not a triangle itself , a+b>c here a+b = c)
So only possible triangle here is 3,4,5
But if numbers get tough this approach will not be easy, algebraic way will be better
By using this method we will able to save time
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a, b, and c are sides of a right triangle. What is the area of the tri 29 Jan 2016, 21:50
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Bunuel
a, b, and c are sides of a right triangle. What is the area of the triangle?

(1) a = 4.
(2) a + b + c = 12
Show more

Statement 1 allows for creating any right triangle one side of which is 4 long. The area can be anything.

Insufficient.

Statement 2 allows for the creation of various right triangles with various areas.

Insufficient.

Combining the statements we know the following.

4 cannot be the hypotenuse as the hypotenuse must be the longest side, and the remaining 8 cannot be divided into 4 and 4 as doing that would not create a right triangle.

As soon as 4 is used for one of the sides, we have 8 left.

3, 4 and 5 work for the two sides and the hypotenuse.

If we increase the length of the 3 side and reduce the length of the hypotenuse, then a² + b² will be greater than c².

If we decrease the length of the 3 side and increase the length of the hypotenuse, then a² + b² will be less than c².

So once the perimeter is defined and the length of one side is defined, the lengths of the other side and the hypotenuse are defined.

The correct answer is C.
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a, b, and c are sides of a right triangle. What is the area of the tri 30 Aug 2021, 03:59
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